Apr 24, 2013

Figure 1: Schematic illustration of the magnification of PS1-10afx. A massive object between us and the supernova bends light rays much as a glass lens can focus light. As more light rays are directed toward the observer than would be without the lens, the supernova appears magnified. Credit: Kavli IPMU

A team of researchers at the Kavli IPMU led by Robert Quimby has identified what may prove to be the first ever Type Ia supernova (SNIa) magnified by a strong gravitational lens. In this work, the 'standard candle' property of Type Ia supernovae is used to directly measure the magnification due to gravitational lensing. This provides the first glimpse of the science that will soon come out of dark matter and dark energy studies derived from deep, wide-field imaging surveys.

The supernova, named PS1-10afx, was discovered by the Panoramic Survey Telescope & Rapid Response System 1 (Pan-STARRS1). PS1-10afx exploded over 9 billion years ago, which places it far further than typical Pan-STARRS1 discoveries. Based on this distance and its relatively bright appearance, the Pan-STARRS1 team concluded that PS1-10afx was intrinsically very luminous. The inferred luminosity, about 100 billion times greater than our Sun, is comparable to members of a new, rare variety of superluminous supernovae (SLSNe), but that is where the similarities end.

SLSNe typically have blue colors, and their brightness changes relatively slowly with time. PS1-10afx on the other hand was rather red even after correcting for its redshift, and its brightness changed as fast as normal supernovae. There is no known physical model that can explain how a supernova could simultaneously be so luminous, so red, and so fast.

Figure 2: The light curve of PS1-10afx compared to a normal SNIa. The blue dots show the observations of PS1-10afx through a red (i-band) filter, which corresponds to ultra-violet (UV) light in the rest frame of the supernova. The red squares show UV observations of the nearby SNIa, 2011fe compressed slightly along the time axis to match the width of PS1-10afx in its rest frame. The dashed lines show a fit to the SN 2011fe data and this same curve shifted by a constant factor of 30. The good agreement with the PS1-10afx data shows that PS1-10afx has the lightcurve shape of a normal SNIa, but it is 30 times brighter than expected.

Soon after the findings were announced, Robert Quimby, a postdoctoral researcher at Kavli IPMU, independently analyzed the data. Quimby is an expert in SLSNe and has played a key role in their discovery. He quickly confirmed part, but not all of the conclusions. PS1-10afx was indeed rather distinct from all known SLSNe, but the data struck Quimby as oddly familiar. He compared the features seen in the spectra of PS1-10afx to known supernova, and, surprisingly, found an excellent match. The spectra of PS1-10afx are almost identical to normal SNIa.

SNIa have a very useful property that has enabled cosmologists to chart the expansion of our Universe over the last several billion years: SNIa have strikingly similar peak luminosities that can be rendered even more standard by correcting for how quickly they brighten and fade (their "light curves"). This property allows astronomers to use SNIa as standard candles to measure distances, as was key to the discovery of the accelerating expansion of the Universe (2011 Nobel Prize in Physics).

How does the light curve of PS1-10afx compare to SNIa? After correcting for time dilation (another consequence of our expanding Universe), the light-curve of PS1-10afx is perfectly consistent with a SNIa, but the observed brightness of PS1-10afx is far too high for such a distant SNIa (see Figure 2).

To understand this mysterious discovery, Quimby tapped into cosmologists and mathematicians at Kavli IPMU, including Marcus Werner who specializes in mathematical theory of gravitational lensing, and found an explanation: the anomalously high brightness could indicate that PS1-10afx was gravitationally lensed by an object between us and the supernova. While light travels through space in "straight" lines, massive objects warp space and thus cause rays of light to "bend" around them. Thus if there is a sufficiently massive object aligned between us and PS1-10afx, light rays that would have gone off to other parts of the cosmos will be focused on us, making PS1-10afx appear brighter (see Figure 1). This does not change the colors or spectra of the lensed object, nor does it change how fast the supernova evolves. The supernova simply appears brighter than it would otherwise, just as was observed for PS1-10afx. In this case, the lensing object may be detectable even after the supernova has faded away; future observations may thus provide final confirmation of this scenario.

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The Kavli IPMU team's identification of the first strongly lensed SNIa is unprecedented but not entirely unexpected. Masamune Oguri, one of the co-authors on Quimby's team, led a paper a few years ago predicting that Pan-STARRS1 was capable of discovering strongly lensed SNIa. He has also shown that such objects may be exploited to place precise constraints on the cosmology of the Universe. Now that Quimby's team has shown how to identify them, next generation surveys with the Hyper Suprime-Cam on Subaru Telescope and the planned LSST can be tuned to discover even more strongly lensed SNIa. These discoveries can be used to study the nature of dark matter, test theories of gravity, and help reveal what our universe is made of.

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User comments : 44

To understand this mysterious discovery, Quimby tapped into cosmologists and mathematicians at Kavli IPMU, including Marcus Werner who specializes in mathematical theory of gravitational lensing, and found an explanation: the anomalously high brightness could indicate that PS1-10afx was gravitationally lensed by an object between us and the supernova. While light travels through space in "straight" lines, massive objects warp space and thus cause rays of light to "bend" around them.

This seems to be the familiar effect of curve space according to Einstein general relativity; anyway the theory cannot explain how empty space could be curved? Maybe this physical view could help…http://www.vacuum...18〈=en

This seems to be the familiar effect of curve space according to Einstein general relativity; anyway the theory cannot explain how empty space could be curved? Maybe this physical view could help

It's easier to visualize if you ignore the distance aspect and only consider the time aspect (since time and distance are inextricably linked). Time slows down when you get closer to the center of a gravitational field. If you imagine two balls linked together with a rod traveling sideways through a gravitational field, the one nearer the center will slow down relative to the one farter away (from the perspective of an outside observer). Therefore they will appear to turn towards the center of the gravity, though an inertial sensor on either ball will register no change in velocity vector.

On a side note:

This is a good demonstration of why it is incomplete and incorrect to visualize expansion as increasing distance between objects. Time must change with and in proportion to distance

Here's another analogy that will set Qstar and Fleetfoot going about the expansion thing again. I promise I'm not trolling. I sinscerely think you guys, and most laypeople, are missing an important point about expansion.

First you must realize that expansion is the exact opposite effect of entering a gravitational field. Get close to a center of mass and time slows down, distance shortens, and mass increases. These three things must all change in proportion to each other or you're breaking all kinds of laws.

So in a variation of my previous post's example, take two balls and a rod falling one end down, directly into a gravity well. The 'bottom' ball will slow down relative to the 'top' ball, but they are still connected by the rod. The speed of light must remain the same, so the distance between them must decrease along with the slowing of time. In the case of a BH event horizon this effect would be large, though we can measure it even here in Earth orbit.

This is a good demonstration of why it is incomplete and incorrect to visualize expansion as increasing distance between objects. Time must change with and in proportion to distance

No. Not so, not "with" and not "in" proportion. It's why spacetime and expanding space, are so counter intuitive. Time and space change as an inverse proportion, Time lengthens (dilation) and space shortens (contraction),

Time and space are still separate qualities, it's only that the change to either must reflect a change in the other. And then only to equalize different reference frames. Time and space can still be considered as separate, as long as the time-like calculations and the space-like measurements are made from a single reference frame.

Here's another analogy that will set Qstar and Fleetfoot going about the expansion thing again. I promise I'm not trolling. I sinscerely think you guys, and most laypeople, are missing an important point about expansion.

I'm hardly a lay person. But be that as it may. Ya are missing an important point. The expansion of the universe is a separate phenomenon than spacetime curvature in the presence of matter.

Time and space change as an inverse proportion, Time lengthens (dilation) and space shortens (contraction)

Time slows as space shortens. This is like contraction which is equivalent to entering a gravitational field.

Time speeds up as space expands. This is like expansion which is equivalent to leaving a gravitational field.

The factor in the equations that defines the amount of difference between any two reference frames is called the Scale Factor. You can move the scale factor around and apply it to any term in the equations; time, distance, energy (mass), etc.

First you must realize that expansion is the exact opposite effect of entering a gravitational field. Get close to a center of mass and time slows down, distance shortens, and mass increases. These three things must all change in proportion to each other or you're breaking all kinds of laws.

Only for an outside observer. The place in spacetime, and the momentum are invariant for ALL observers. The space and the time are variable but only from different reference frames. The momentum will always be invariant regardless of frame.

This was not a "gravitational lens". To begin with, to apply the term "lens" to this phenomenon is misleading. They might divert some light from a distant object into a converging path, but not all of it. Glass lenses and such work with all the light from the source, they don't absorb any of it. All these "lenses" have done so far is to twist or multiply the perceived images of a distant object, but they never magnified or intensified the light. Something else caused the light to be brighter than expected.

Ya are missing an important point. The expansion of the universe is a separate phenomenon than spacetime curvature in the presence of matter

No, you are missing the most important point of all. The expansion/contraction of spacetime is a consequence of the presence of matter, and the two are equivalent. If you do not see that expansion/contraction are exactly the same as local curvature of spacetime in the presence of mass, then you're missing the whole connection between GR and Lambda-CDM. Without that connection, there's no need for dark matter or energy. And you call yourself a non-layperson?

Time slows as space shortens. This is like contraction which is equivalent to entering a gravitational field.

Time speeds up as space expands. This is like expansion which is equivalent to leaving a gravitational field.

That only relates to the spacetime in the pretense of matter. Empty space expands by different rules. They are not the same phenomena. General Relativity deals with this difference. Ya seem to be hung up with the Special Relativity and the spacetime posited there. Space expands irrespective of time. Space curves in relation to time only in the presence of matter. They are separate phenomena.

No, you are missing the most important point of all. The expansion/contraction of spacetime is a consequence of the presence of matter, and the two are equivalent. If you do not see that expansion/contraction are exactly the same as local curvature of spacetime in the presence of mass, then you're missing the whole connection between GR and Lambda-CDM. Without that connection, there's no need for dark matter or energy. And you call yourself a non-layperson?

I do, and I've probably only read some 1000's of tomes on relativity and cosmology. The expansion of space is entirely independent of spacetime curvature caused by the presence of matter. That is why we find the universe to be flat on cosmic scales, On cosmic scales there is no net spacetime curvature. Spacetime curvature is only manifest where there is matter. The expanding space contains no matter, it is linear and flat, it has no spacetime curvature.

Gravitational warping of spacetime is a phenomena that only exists in the presence of matter.

Space expansion is independent of spacetime warping.

The expanding space contains no new matter, no old matter, it is just space. And since it contains no matter, nothing which carries momentum, time is not a function which affects it. All matter lives in spacetime, But all space does not contain matter. That space is the same for all observers from any reference frame at any time. The ONLY thing that changes is the volume it occupies, it has no other attribute.

Only for an outside observer. The place in spacetime, and the momentum are invariant for ALL observers

For an outside observer, or as observed between two observers. We see this with GPS signals. Observers here on Earth would say that GPS satellite clocks run slightly too fast, while the GPS satellites would say that our clocks at the surface are slightly too slow.

That only relates to the spacetime in the pretense of matter. Empty space expands by different rules.

That is 100% wrong. It is exactly the same thing. Spacetime distortion is spacetime distortion. There's not two kinds of spacetime dilation (distortion). They are exactly equivalent.

Ya seem to be hung up with the Special Relativity and the spacetime posited there

No, you seem to be hung up with not understanding the concept of a co-moving coordinate system. The way you are treating it is only relevant if you simplify it down to non-comoving coordinates, which isn't reality.

That's where you've been wrong from the start. If you think that reference frames apply at small scales, such as a gravity well, but do not apply at large scales such as expansion of the universe at different times, then you are using a non-realistic simplification known as proper distance. In your non-realistic version of expansion, they use a fixed 'scale factor', which isn't how expansion works.

Gravitational warping of spacetime is a phenomena that only exists in the presence of matter.

Space expansion is independent of spacetime warping

No, and in fact, the shape of the curvature and speed/direction of expansion/contraction is determined by the total mass of the universe and its distribution over large scales. It is non-uniform on small scales, but seems to be nearly homogeneous at larger scales. It is all related to mass/energy though.

That only relates to the spacetime in the pretense of matter. Empty space expands by different rules.[

That is 100% wrong. It is exactly the same thing. Spacetime distortion is spacetime distortion. There's not two kinds of spacetime dilation (distortion). They are exactly equivalent.

What is 100% wrong is your conflating two different things. Spacetime only relates to momentum (matter-energy). Space devoid of matter-energy is a separate entity. If matter-energy is absent (as in the pure space of expansion) there is only space, flat void space, and nothing to put into the spacetime metrics.

It's why General Relativity has separate "space-like" solutions, and "time-like" solutions. Ya can separate space from time descriptions, as long as one is held constant. We do it every day in every class, in every lab, on every telescope.

Ya are "blindly parroting" the popular account without truly understanding the nuances. Space, time & spacetime are each separate & real.

No, you seem to be hung up with not understanding the concept of a co-moving coordinate system. The way you are treating it is only relevant if you simplify it down to non-comoving coordinates, which isn't reality.

I'm hung up only on the Standard Cosmology and General Relativity. EVERYTHING I have posted is entirely consistent and "mainstream" with them.

That's where you've been wrong from the start. If you think that reference frames apply at small scales, such as a gravity well, but do not apply at large scales such as expansion of the universe at different times, then you are using a non-realistic simplification known as proper distance.

I am using the the very realistic and consensus view. If ya want to posit "new" physics, then do so, but claim that your new physics are actually supported by General Relativity. They are not.

Ya seem have misinterpreted the things ya've read. My point of view is the consensus (by a huge majority) of everything taught today.

All these "lenses" have done so far is to twist or multiply the perceived images of a distant object, but they never magnified or intensified the light. Something else caused the light to be brighter than expected

Qstar already correctly covered this, but you should at least look up a wiki on this, though the pictures embeded in this story should be enough.

The way light works is that you only see light that is headed directly from an object to your eye. If you place a lense in front of your eye, you can gather light from a wider area and focus that light down to the size of your eye. This packs more light from the source into your eye. You can call this 'brightening' or 'magnifying' depending on what you're doing. It amounts to the same thing though.

So, do you see now? If not, then please do a google and look up some wiki pages. The wiki on lenses should be pretty good, since it's a simple topic.

If matter-energy is absent (as in the pure space of expansion) there is only space, flat void space, and nothing to put into the spacetime metrics

No, you are describing something outside the Universe. The very existence of space is the Universe, and time is a property of space. You can't have space without a time scale factor. Every bit of space at every time has a scale factor. The scale factor is dependent on distribution of mass/energy. It's never zero or infinity, not in the Universe anyway.

This is not a lens. No such gravitational system is a lens. Remember that the lensing caused by gravitational fields associated with matter involves light coming from beyond the matter. And light on the other side of matter is absorbed by the matter. Q-Star inly demonstrates their lack of understanding of the subject by invoking the inconsequential about glass lenses absorbing some light. The amount of light absorbed by glass lenses is so small compared to that absorbed by gravitationally lensing that it renders Q-Star's "contradiction" laughable. Add, too, that no other gravitational lens has magnified the light from sources. In fact, no lens magnifies the amount of light, only the size of the object, and that can tend to dilute the light per unit area.

The Universe is nearly flat today, and expansion has nearly stopped. In the distant past the Universe was extremely curved, then inflation happened and it flattened out. Expansion is the same as local curvature at large scales.

The overall mass/energy of the Universe determines whether the Universe will collapse back down to infinite curvature again or not. This would be the Big Crunch. When you say the Universe is flat, that only means that it has expanded out so much that the observable part of the Universe is so flat that it's impossible to tell the difference. Kinda like the analogy of a balloon that's infinitely big. The surface would appear flat.

Expansion represents a change in the curvature of spacetime. Before the inflation period, the curvature would have been measurable on smaller scales, and would manifest itself in exactly the same way that we see small scale changes in curvature due to massive objects.

Re: "There is no known physical model that can explain how a supernova could simultaneously be so luminous, so red, and so fast."

"known physical model" should be replaced with "accepted physical model". What if redshift is a function of age instead of velocity, as Halton Arp has suggested? It's one thing to disagree with Arp, but perhaps a little bit self-serving to pretend as though he never actually postulated an alternative explanation for redshift ...

The "matter" density of the glass lens is so much greater than the "matter" density of the gravitational lens would lead ya to think,,,, what? Right ya are, the gravitational lens would actually absorb less.

Q-Star inly demonstrates their lack of understanding of the subject by invoking the inconsequential about glass lenses absorbing some light.

Do the maths and see how much understanding ya might be lacking.

The amount of light absorbed by glass lenses is so small compared to that absorbed by gravitationally lensing that it renders Q-Star's "contradiction" laughable.

It is laughable. By your reasoning, we should not see anything out there, there is too much stuff "absorbing" other stuff.

Add, too, that no other gravitational lens has magnified the light from sources.

They all do. That's the very reason they coined the term "gravitational lensing".

The flat part I understand, what model has the "expansion has nearly stopped" in it? Not any of the mainstream models. Accelerating expansion is at the foundation of all currently conventional models .

What new model are ya proposing?

Expansion represents a change in the curvature of spacetime. Before the inflation period, the curvature would have been measurable on smaller scales, and would manifest itself in exactly the same way that we see small scale changes in curvature due to massive objects.

No, expansion represents the addition of space to the universe. Not time, not spacetime, not matter,,, the expansion adds only space. The same matter, and same time scale must conform to the additional space, not the other way around.

Whether a gravitational lens is a black hole or a galaxy, all it takes is an accumulation of matter bigger than the star distant and it will absorb all the light. Density has nothing to do with it. A piece of black construction paper has less density than glass, yet it will absorb more light on the other side than a glass lens would. And, if gravitational lenses don't magnify the intensity of light, which is what this article is talking about, why would this supposed case of magnified light be considered so distinctive?

This is not a lens. No such gravitational system is a lens. Remember that the lensing caused by gravitational fields associated with matter involves light coming from beyond the matter. And light on the other side of matter is absorbed by the matter.

Look at the graphic at the top of the article. The light we see is mostly that which passes around the intervening mass. Note also that galaxies are mostly empty space, the stars block a tiny fraction of any background source, unless it is seen nearly edge-on so that the the light path through the disc is very long.

I promise I'm not trolling. I sinscerely think you guys, and most laypeople, are missing an important point about expansion.

I know you're not trolling but you have a small flaw in your understanding which is causing the disagreement.

.. you seem to be hung up with not understanding the concept of a co-moving coordinate system. The way you are treating it is only relevant if you simplify it down to non-comoving coordinates, which isn't reality.

Actually, he isn't. We talked before about the difference between proper distance and co-moving coordinates. Proper distance is the real separation between objects measured at a given cosmic age, call that R(t) where 't' is the age. By convention we set t=0 to be now.

The scale factor in the Friedmann Equations is a(t) = R(t) / R(0)

The comoving distance is a useful mathematical artefact defined by R(t) / a(t)

It should be obvious then that the comoving distance is just the proper distance today (excluding peculiar motion).

When you say the Universe is flat, that only means that it has expanded out so much that the observable part of the Universe is so flat that it's impossible to tell the difference. Kinda like the analogy of a balloon that's infinitely big. The surface would appear flat.

Expansion represents a change in the curvature of spacetime.

Not quite. Take a balloon and blow it up quite large. Draw a 1mm grid on it as square as you can representing 100MPc distances. Lay a sheet of rigid transparent plastic with a similar grid over the top so the grids line up. Scatter a few random points on the balloon to represent galaxy clusters.

Blow the balloon up a bit more. The distance between the dots read from the rigid sheet is the real, proper distance between the galaxies. That has increased. The grid drawn on the balloon has also expanded, the lines are no longer 1mm apart but each dot is at the same grid location (comoving coordinates). The surface has flattened, but also expanded.

The flat part I understand, what model has the "expansion has nearly stopped" in it? Not any of the mainstream models. Accelerating expansion is at the foundation of all currently conventional models .

What new model are ya proposing?

Okay, I'm getting bored with your lack of understanding, and you're starting to border on rudeness, even though you're the one who doesn't get basic math.

Look: The scale factor determines the amount of expansion at any given time. You can apply it to any term in the equations.

IMPORTANT:As with any form of math, if you change the scale factor, like multiply it by 2, you MUST do the same thing to the other side of the equation.

If you do not, then E is not equal to mC^2 and all kinds of other violations happen. You cannot break the laws of physics. Expansion obeys these laws.

I'm getting bored with your lack of understanding, and you're starting to border on rudeness, even though you're the one who doesn't get basic math.

I'm sorry ya feel that way. By the By: I teach, and have taught calculus based physics classes to astrophysics majors for a couple of decades. I know the basic maths.

If you do not, then E is not equal to mC^2 and all kinds of other violations happen. You cannot break the laws of physics. Expansion obeys these laws.

Ya are conflating the GR & the Lambda CDM, the Concordant Model of Cosmology. They must agree, true. But what ya are missing is they address two separate questions. GR is model of gravitation, how matter interacts with matter. It is not a theory of cosmology, that association only came as an afterthought. The E = mc^2 has nothing to do with this, it is an inaccurate oversimplification for laymen.

I'm assuming that he's talking about how the universe was expanding at a decreasing rate and then switched to an increasing rate billions of years ago.

I also assume he means that the acceleration of expansion approached zero (i.e., the universe would be expanding at a constant velocity temporarily) before starting to increase, however, I have never heard of this before. Granted, I'm a layman on these issues.

Durring inflation, the 'slope' representing the rate of expansion was nearly vertical. After inflation ended, somewhere around 400 million yr after the BB, the slope leveled off to nearly zero. That slope has just recently started to increase again, representing acceleration of expansion, but that's very recent. Any light we see that's coming from less than 13 billion LY away, hasn't done much expansion. More than 90% of the expansion happend in the first 3% of time. The remaining 97% of time would be nearly free of expansion if not for the acceleration that started in the last couple billion years.

The far left depicts the earliest moment we can now probe, when a period of "inflation" produced a burst of exponential growth in the universe. (Size is depicted by the vertical extent of the grid in this graphic.) For the next several billion years, the expansion of the universe gradually slowed down as the matter in the universe pulled on itself via gravity

If you aren't familiar with this timeline or what it means, then I can understand why you are confused about some of the more complicated parts of the Lambda-CDM model.

Durring inflation, the 'slope' representing the rate of expansion was nearly vertical. After inflation ended, somewhere around 400 million yr after the BB, the slope leveled off to nearly zero. That slope has just recently started to increase again, representing acceleration of expansion, but that's very recent.

It has never quit expanding. It's only accelerated.

Any light we see that's coming from less than 13 billion LY away, hasn't done much expansion. More than 90% of the expansion happend in the first 3% of time..

That is just not so. The redshift is the expansion manifested in the light. If it wasn't being significantly expanded, there would be no redshift, unless ya hold to the "tired light" theory.

The wiki picture is an oversimplification in two dimensions. Ya are seeing things in that illustration that are not there.

You're right that the universe never stopped expanding and that it never stopped accelerating it's expansion. But the rate of acceleration was decreasing until about 4.5 BY ago (if my memory is correct). Since that time, the rate of acceleration (dx^3/dt not dx^2/dt, which is just acceleration) has been increasing.

What he has claimed is that this rate of acceleration approached zero before increasing. That's what I've never heard of before.

The far left depicts the earliest moment we can now probe, when a period of "inflation" produced a burst of exponential growth in the universe.

(Size is depicted by the vertical extent of the grid in this graphic.) No need to insert commentary in quotes.

For the next several billion years, the expansion of the universe gradually slowed down as the matter in the universe pulled on itself via gravity

VERY GRADUALLY SLOWED doesn't mean "almost stopped".

If you aren't familiar with this timeline or what it means, then I can understand why you are confused about some of the more complicated parts of the Lambda-CDM model.

But that is the point, I am not confused. Ya've become so sure that reading popular accounts has given ya true understanding ya can't see that the popular accounts ALWAYS carry the fault of missing the nuances & finer points. That leads to confusion & misunderstandings.

You're right that the universe never stopped expanding and that it never stopped accelerating it's expansion. But the rate of acceleration was decreasing until about 4.5 BY ago (if my memory is correct). Since that time, the rate of acceleration (dx^3/dt not dx^2/dt, which is just acceleration) has been increasing.

What he has claimed is that this rate of acceleration approached zero before increasing. That's what I've never heard of before.

Correct Sir. The acceleration slowed, not the expanding,,,, it has ALWAYS been ACCELERATING, it just picked up the pace a few billion years ago.

I also assume he means that the acceleration of expansion approached zero (i.e., the universe would be expanding at a constant velocity temporarily) before starting to increase, however, I have never heard of this before. Granted, I'm a layman on these issues.

But he stated the expansion slowed almost to a halt. That is where he is missing the picture of expanding space and the present distances of objects we "see" at high z. The acceleration slowed. Not the expansion.

Consider expansion as driving to the store. Just after the big bang, ya hit the gas with turbo-boosters, in three seconds ya are doing 100 mph. Ya let up, not off, the gas, ya are still going 100 plus mph. (expanding).

Ya might even be accelerating just a little but all that means is ya are going 100 plus mph (expanding). After a bit, ya want to really pour it on, and hit the floor, now ya are accelerating again. Expanding faster. But ya never were going slower than 100 mph (expanding),

The more I think about it, I was wrong about the dx^3/dt; it's just the dx^2/dt. The acceleration was decreasing (not velocity, velocity was still increasing) until about 5 BY ago. At that point the acceleration began increasing and has been ever since.

I think Swift understands this; I just think it was the words he used that created a confusion.

The acceleration was decreasing (not velocity, velocity was still increasing) until about 5 BY ago. At that point the acceleration began increasing and has been ever since.

There is certainly a little confusion here.

1. Inflation only lasted about 10^-32 seconds.

2. After inflation ended, the universe was radiation dominated until it was about 47,000 years old. During that period, the scale factor was proportional to the square root of time or t^(1/2).

3. From 47 thousand years to about 9.5 billion years, it was matter dominated and the scale factor varied as t^(2/3). In both those eras, the expansion was decelerating but about 4 billion years ago, the rate reached a minimum and since then it has started expanding.

4. For the last 4 billion years it has been dark energy dominated and is changing towards the de Sitter model.

Whether the minimum rate can be described as "nearly stopped" or not is a matter of opinion, science has no rigid definition of "nearly".

Note there is an error in that diagram. The first stars were ionising the ISM by about 130 million years (z=25) according to the WMAP data (not the graphic) and some simulations put the very first stars at z=65 or about 32 million years.

2. After inflation ended, the universe was radiation dominated until it was about 47,000 years old. During that period, the scale factor was proportional to the square root of time or t^(1/2).

3. From 47 thousand years to about 9.5 billion years, it was matter dominated and the scale factor varied as t^(2/3). In both those eras, the expansion was decelerating but about 4 billion years ago, the rate reached a minimum and since then it has started expanding.

4. For the last 4 billion years it has been dark energy dominated and is changing towards the de Sitter model.

Whether the minimum rate can be described as "nearly stopped" or not is a matter of opinion, science has no rigid definition of "nearly".

Ya are absolutely correct. But one point, the expansion never stopped, otherwise we would see a period of collapse.

Ya Sir, are so much better than I on this venue, I find it a difficult area to express myself in.

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